I too have used the same 'resource', I think from what I remember if you are just talking about SEGA/Mega CD there is only a .cue + single .bin for most if not all games anyway, even if they have audio tracks. Everything is inside one .bin, but the references to the track start/finish points are stored within the .cue. PSX is the platform where there is a right mix of single and multiple files, Ridge Racer for example has quite a lot and you have to launch from the .cue file for it to work properly.
There must be a simple explanation why you are unable to launch .cue files with lr-genesis-plus-gx, as like I say, mine works absolutely fine. If it does become an issue let me know and I will send you a excerpt of my config so you can compare.
Cheers